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Push a wheelchair forward, or stop a moving ball. In one case your force helps the motion, in the other it fights it. Work can carry a sign.
- Positive work: displacement is in the same direction as the force — e.g. pushing a wheelchair, the force and displacement point the same way.
- Negative work: displacement is opposite to the force — e.g. a goalkeeper stopping a ball pushes against the ball's motion.
- Work has no direction ; it is just a number carrying a + or − sign .
- Positive work — work done by a force when the displacement is in the same direction as the force.
- Negative work — work done by a force when the displacement is in the direction opposite to the force.
A girl lifts a dumbbell and slowly lowers it. When does she do positive work and when negative?
Lifting up: her force (up) is in the direction of displacement (up) → positive work .
Lowering down: her force (up, holding it) is opposite to the displacement (down) → negative work .
A goalkeeper's hand moves back 15 cm while applying 200 N to stop a ball. How much work does she do on the ball?
The force opposes the ball's motion, so the displacement is taken as negative.
W
= F × s
= 200
N
× (-0.15
m
)
= -30
J
. The goalkeeper does
−30 J
of work on the ball.
- The ball and the goalkeeper apply equal and opposite forces on each other, so both do work on each other: the ball does positive work on the goalkeeper, while the goalkeeper does negative work on the ball.
- 1. Weightlifter holding a barbell steady: no work is done on the barbell, because there is no displacement (even though holding it is tiring).
- 2. Friction on coins sliding on a rough surface: friction acts opposite to the motion, so the work done by friction is negative .
NCERT Question 1 — State whether True or False
State whether True or False.
(i) Work is said to be done when a force is applied, even if the object does not move.
(ii) Lifting a bucket vertically upward results in positive work done on the bucket.
(iii) The SI unit for both work and energy is joule (J).
(iv) A motionless stretched rubber band has kinetic energy.
(v) Energy can change from one form to another.
NCERT Question 2 — Fill in the blanks
Fill in the blanks.
(i) Work done = ______ × ______ (in the direction of force).
(ii) 1 joule of work is done when a force of ______ newton displaces an object by 1 metre in the direction of the force.
(iii) The expression for kinetic energy of a body of mass m and velocity v is ______.
(iv) The potential energy of an object of mass m at a small height h from the Earth's surface is ______.
(v) Power is defined as the ______ at which work is done.
NCERT Question 10 — A ball of mass 2
A ball of mass 2 kg is thrown up with a velocity of 20 m s⁻¹. (i) Identify the sign of the work done by gravity on the ball during its upward motion and its downward motion. (ii) If the ball reaches a height of 19.4 m, how much work was done by air resistance (assume g = 10 m s⁻²).
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A porter holds a suitcase steady on his head and stands still. How much work does he do on the suitcase?
Show Answer
Zero. There is no displacement (s = 0), so W = F × s = 0 — even though he feels tired. -
What is the SI unit of work done, and how is 1 joule defined?
Show Answer
The joule (J). 1 J of work is done when a force of 1 N displaces an object by 1 m in the direction of the force. -
A goalkeeper stops a ball. Is the work she does on the ball positive or negative?
Show Answer
Negative — her force is opposite to the ball's displacement. -
How can the work done be found when the force is
not
constant?
Show Answer
By finding the area under the force-displacement graph between the initial and the final positions.
